Reflections and Asymptotes in Functions

The video tutorial explains how to graph reflections of exponential functions. It covers vertical reflections by multiplying the function by a negative coefficient, resulting in a reflection over the x-axis. It also discusses horizontal reflections by using a negative exponent, leading to a reflection over the y-axis. Key points and transformations are identified to aid in graphing these functions.

What is the base of the exponential function discussed in the introduction?

• -2

• 2

• -1

• 1

What does a negative sign in front of an exponential function indicate?

• Horizontal shift

• Vertical reflection

• No change

• Scaling

How are the y-values affected by the negative sign in the function?

• They are multiplied by -1

• They are doubled

• They are halved

• They remain unchanged

What happens to the graph when it is flipped upside down?

• It reflects over the y-axis

• It moves to the right

• It moves to the left

• It reflects over the x-axis

Where is the horizontal asymptote located for the function discussed?

• y = 2

• y = 1

• y = 0

• y = -1

What type of reflection occurs when the negative sign is attached directly to x?

• Horizontal reflection

• Vertical reflection

• No reflection

• Diagonal reflection

How does the negative sign affect the x-values in a horizontal reflection?

• They are doubled

• They are halved

• They remain unchanged

• They are multiplied by -1

What is the behavior of the graph as it approaches the x-axis in a horizontal reflection?

• It remains constant

• It decreases without bound

• It increases without bound

• It oscillates

Which axis does the graph reflect over in a horizontal reflection?

• y-axis

• No axis

• z-axis

• x-axis

What is an alternative way to express the function 2 to the negative x power?

• 2 raised to the negative x power

• 1/2 raised to the x power

• 2 raised to the x power

• 1/2 raised to the negative x power